PHYS 5326 – Lecture #9 & 10
Friday, Feb. 21, 2003
Dr. Jae Yu
1. Interpretation of Sin2qW results
2. The link to Higgs
3. Neutrino Oscillation
•Next makeup class is Friday, Mar. 14, 1-2:30pm, rm 200.
Friday, Feb. 21, 2003
PHYS 5326, Spring 2003
Jae Yu
1
SM Global Fits with New Results
Without NuTeV
c2/dof=20.5/14: P=11.4%
With NuTeV
c2/dof=29.7/15: P=1.3%
Confidence level in upper
Mhiggs limit weakens slightly.
LEP EWWG: http://www.cern.ch/LEPEWWG
Friday, Feb. 21, 2003
PHYS 5326, Spring 2003
Jae Yu
2
Tree-level Parameters: r0 and sin2qW(on-shell)
sin2 θ W  0.2265  0.0031
ρ 0  0.9983  0.040
2 (On  shell)
W
δsin θ
 M 2t  175GeV 2 

 0.00022  
2



50GeV


 MH 
 0.00032  ln

 150GeV 
• Either sin2qW(on-shell) or r0 could agree with SM but both agreeing
simultaneously is unlikely
Friday, Feb. 21, 2003
PHYS 5326, Spring 2003
Jae Yu
3
Model Independent Analysis
• Rn`n can be expressed in terms of quark couplings:
- 
 - 

 n N  n X 
  g2  r 1g2
Rn n   - 
L
R


 n N      X 


σ νN    X
1
r


Where
σ νN     X
2




Paschos-Wolfenstein formula can be expressed as
R 
ν
ν
σNC
 σNC
ν
ν
σ CC
 σ CC
Friday, Feb. 21, 2003
ν
ν
1
R

rR


 ρ2   sin2θ W  
 gL2  gR2
1 r
2

PHYS 5326, Spring 2003
Jae Yu
4
Model Independent Analysis
• Performed a fit to quark couplings (and gL and gR)
– For isoscalar target, the nN couplings are
5 4 
1
2
g  u  d  ρ   sin θ W  sin θ W 
9
2

2
2
2
2 5
4
gR  uR  dR  ρ0 sin θ W
9
exp
exp
R
– From two parameter fit to Rn and n
2
L
2
L
2
L
2
0
gL2  0.3005  0.0014 (SM: 0.3042 -2.6 deviation)
g  0.0310  0.0011 (SM: 0.0301  Agreement)
2
R
Friday, Feb. 21, 2003
PHYS 5326, Spring 2003
Jae Yu
5
Model Independent Analysis
Difficult to explain the
disagreement with SM by:
Parton Distribution Function or
LO vs NLO or Electroweak
Radiative Correction: large
MHiggs
Friday, Feb. 21, 2003
PHYS 5326, Spring 2003
Jae Yu
6
What is the discrepancy due to (Old Physics)?
• R- technique is sensitive to q vs`q differences
and NLO effect
– Difference in valence quark and anti-quark
momentum fraction
• Isospin symmetry assumption might not be
entirely correct
– Expect violation about 1%  NuTeV reduces this
effect by using the ratio of n and `n cross sections
 Reducing dependence by a factor of 3
Friday, Feb. 21, 2003
PHYS 5326, Spring 2003
Jae Yu
7
What is the discrepancy due to (Old Physics)?
• s vs`s quark asymmetry
– s and `s needs to be the same but the momentum
could differ
• A value of Ds=xs -x`s ~+0.002 could shift sin2qW by 0.0026, explaining ½ the discrepancy (S. Davison, et. al.,
hep-ph/0112302)
• NuTeV di-m measurement shows that Ds~-0.0027+/-0.0013
Use opposite sign di-m events
to measure s and `s.
Friday, Feb. 21, 2003
PHYS 5326, Spring 2003
Jae Yu
8
What is the discrepancy due to (Old Physics)?
• NLO and PDF effects
– PDF, mc, Higher Twist effect, etc, are small changes
• Heavy vs light target PDF effect (Kovalenko et al., hepph/0207158)
– Using PDF from light target on Iron target could make up the
difference  NuTeV result uses PDF extracted from CCFR
(the same target)
Friday, Feb. 21, 2003
PHYS 5326, Spring 2003
Jae Yu
9
nens Oscillations with Large Mn
• LSND result implicate a large Dm2 (~10 — 100eV2)
solution for ne oscillation MiniBooNe at FNAL is
running to put the nail on the coffin
• How would this affect NuTeV sin2qW?
1 R  rR
 
2
1 r
ν
sin θ W
2
ν
and
Rn 
NnShort  NnMC
e
NnLong

MC
MC
P
N

N
P

N
If nens with n e n s then n e
n e n e n e
n e 1- Pn e n s

Thus, MC will subtract more than it is in nature, causing
measured Rn to be smaller and thereby increasing sin2qW
Friday, Feb. 21, 2003
PHYS 5326, Spring 2003
Jae Yu
10
New Physics: Interactions from Extra U(1) – Z’
• Extra U(1) gauge group giving
rise to interactions mediated
by heavy Z’ boson (MZ’>>MZ)
• While couplings in these
groups are arbitrary, E(6)
gauge groups can provide
mechanism for extra U(1)
interaction via heavy Z’.
• Can give rise to gR but not gL
which is strongly constrained
by precision Z measurement
Friday, Feb. 21, 2003
PHYS 5326, Spring 2003
Jae Yu
11
What other explanations (New Physics)?
• Heavy non-SM vector boson
exchange: Z’, LQ, etc
– Suppressed Znn (invisible)
coupling
– LL coupling enhanced than LR
needed for NuTeV
Both precision data
are lower than SM
Friday, Feb. 21, 2003
PHYS 5326, Spring 2003
Jae Yu
12
What other explanations (New Physics)?
• Propagator and coupling corrections
– Small compared to the effect
• MSSM : Loop corrections wrong sign and small for
the effect
• Many other attempts in progress but so far nothing seems
to explain the NuTeV results
– Lepto-quarks
– Contact interactions with LL coupling (NuTeV wants mZ’~1.2TeV, CDF/DØ:
mZ’>700GeV)
– Almost sequential Z’ with opposite coupling to n
Langacker et al, Rev. Mod. Phys. 64 87; Cho et al., Nucl. Phys. B531, 65; Zppenfeld
and Cheung, hep-ph/9810277; Davidson et al., hep-ph/0112302
Friday, Feb. 21, 2003
PHYS 5326, Spring 2003
Jae Yu
13
Linking sin2qW with Higgs through Mtop vs MW
One-loop
correction to
sin2qW
 shell)
δsin2 θ(On
W
Friday, Feb. 21, 2003
 M 2t  175GeV 2 
 MH 

 0.00022  

0.00032

ln


2

 150GeV 
 50GeV 

PHYS 5326, Spring 2003
Jae Yu
14
Neutrino Oscillation
• First suggestion of neutrino mixing by B. Pontecorvo at the
K0, K0-bar mixing in 1957
• Solar neutrino deficit in 1969 by Ray Davis in Homestake
Mine in SD.  Called MSW effect
• Caused by the two different eigenstates for mass and weak
• Neutrinos change their flavor as they travel  Neutrino
flavor mixing
• Oscillation probability depends on
– Distance between the source and the observation point
– Energy of the neutrinos
– Difference in square of the masses
Friday, Feb. 21, 2003
PHYS 5326, Spring 2003
Jae Yu
15
Neutrino Oscillation Formalism
• Two neutrino mixing case:
n e   cosq
   
n   sin q
 m 
sin q n1 
 
cosq n 2 
OR
n e  cosq n 1  sin q n 2
n m   sin q n 1  cosq n 2
where n e and n m are weak eigenstates, while
n 1 and n 2 are mass eigenstates, and q is the
mixing angle that give the extent of mass
eigenstate mixture, analogous to Cabbio angle
Friday, Feb. 21, 2003
PHYS 5326, Spring 2003
Jae Yu
16
Oscillation Probability
• Let nm at time t=0 be the linear combination of n1 and n2
with masses m1 and m1, the wave function becomes:
n m t  0   sin q n 1  cosq n 2
• Then later time t the nm wave function becomes:
n m t    sin q exp  i E1  t  n 1  cosq exp  i E2  t  n 2






• For relativistic neutrinos (En>>mi), the energies of the
mass eigenstates are:
2
Ek 
Friday, Feb. 21, 2003
p 2  mk2  p 
PHYS 5326, Spring 2003
Jae Yu
mk
2p
17
Oscillation Probability
• Substituting the energies into the wave function:
2
2
 
 
m


i
D
m
t
1
n m t   exp  it  p  2 E   sin q n 1  cosq n 2 exp 
2 En  
n  

 
where Dm2  m12  m22 and En  p.
• Since the n’s move at the speed of light, t=x/c, where x
is the distance to the source of nm.
• The probability for nm with energy En oscillates to ne at
the distance L from the source becomes
 1.27Dm 2 L 

Pn m  n e   sin 2q sin 
En


2
Friday, Feb. 21, 2003
2
PHYS 5326, Spring 2003
Jae Yu
18
Homework Assignments
• Produce an electron ET spectrum of the highest ET electrons
in your samples
– Due Wednesday, Feb. 26
• Complete the derivation of the probability for nm of energy
En to oscillate to ne at the distance L away from the source
of nm.
• Draw the oscillation probability distributions as a function of
– Distance L for a fixed neutrino beam energy En (=5, 50, 150 GeV)
– En for a detector at a distance L (=1.5, 735, 2200km) away from
the source
• Due Wednesday, Mar. 5
Friday, Feb. 21, 2003
PHYS 5326, Spring 2003
Jae Yu
19